Least Common Multiple (LCM) of 64 and 101
The least common multiple (LCM) of 64 and 101 is 6464.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 64 and 101?
First, calculate the GCD of 64 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 101 = 0 remainder 64 |
| 2 | 101 ÷ 64 = 1 remainder 37 |
| 3 | 64 ÷ 37 = 1 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 105 | 15855 |
| 55 and 186 | 10230 |
| 37 and 144 | 5328 |
| 135 and 171 | 2565 |
| 80 and 83 | 6640 |